# The Higgs Boson, in Theory and in Experiment

### Pheno 2012, part 1

As I mentioned in my previous post, I’m at the Phenomenology 2012 Symposium, which thankfully most people just call Pheno 2012. Physics conferences often have a brutal schedule: I attended 21 talks yesterday alone, with more today and Wednesday morning. At this rate, I’ll never blog it all, so I’m not going to try. I’ll highlight a few good talks, and some of the big ideas, though, and hopefully that will give you a flavor of the event.

### The Higgs Boson, in Theory

One of the fundamental ideas in particle physics is symmetry: what happens if you swap one particle for another, or reverse the direction of time in an interaction, and so forth. Physicists are interested both when symmetries are preserved and when symmetries are broken: something that looks like it should be symmetrical, but is not.

The Higgs boson, as I described in an earlier post, was first proposed as a way to understand the difference between the electromagnetic force and the weak nuclear force. These two forces have a lot in common—between the two of them, they control the interactions between leptons (electrons, muons, tauons, and neutrinos), and link leptons to hadrons (the category including protons and neutrons)—but the electromagnetic force is infinite in range, while the weak force has a very short range. Another equivalent way to say it is that the photon, which mediates the electromagnetic force, is massless, while the W and Z gauge bosons, which mediate the weak force, have relatively large masses, and decay rapidly.

Electroweak theory describes the combined physics of both the electromagnetic and weak forces. The weak force involves the three gauge bosons, which are labeled W+, W, and Z0 (often just written as Z). The superscript indicates their electric charges: not only do the bosons interact via the weak force, the W bosons also interact electromagnetically. The W and Z bosons form a triplet analogous to the three possible axes of rotation in a sphere: the math is the same. This type of symmetry is known as SU(2) symmetry, which is related to the math of quaternions. Similarly, the symmetry in electromagnetism is akin to rotations around a single axis, which we call U(1) symmetry.

(As an aside: the underlying theory is something known as Yang-Mills theory, a general set of mathematical tools that helps us connect symmetries to physics. Electromagnetism turns out to be another Yang-Mills theory, though Maxwell and his colleagues developed it nearly 100 years before C. N. Yang and Robert Mills did their work. General relativity is a cousin to Yang-Mills theories, but the equations are different; a lot of my PhD thesis work examined the mathematical underpinnings of these two theories.)

Photons and the W/Z bosons form a larger symmetry (similar to the connection between the spin-0 and spin-1 composites I wrote about in an earlier post), but that symmetry is broken by the massiveness of the weak force gauge bosons. The Higgs boson is an additional field that explains why the W and Z bosons are massive: that extra degree of freedom splits the weak force off from the electromagnetic force. Photons and the W and Z bosons are vector bosons (meaning they are spin-1 particles), but the Higgs is a scalar (spin-0) particle. It is also electrically neutral and decays rapidly, which is an unfortunate combination if you want to detect it in your experiments. (Charged particles can be manipulated using electric and magnetic fields.)

The combination of electroweak physics with the physics of the strong force yields the Standard Model (SM). The Higgs boson is one of the missing pieces of the SM, which is why searching for it is so important to particle physicists: if it is absent, or if it has different properties than those consistent with the SM, then it tells us there must be new physics. The problem is that the SM doesn’t tell us exactly what the Higgs mass (or the mass of any particle) should be! While it establishes some mass relationships, those are pretty broad, which makes Higgs-hunting a big challenge. I’ll return to that idea in the next section.

To make matters worse, the Higgs boson may exist, but have different properties than those predicted by the SM: it might be more massive, less massive, or interact in different ways. (It’s also possible to detect a particle that apes the Higgs in some ways, but is another type of particle entirely.) Once you drift from the Standard Model, it’s akin to studying insects that aren’t beetles: the options proliferate until it’s hard to even know where to begin! Maybe there’s more than one Higgs-like particle that breaks electroweak symmetry; maybe another mechanism entirely is at work. (If I have time and energy, I’ll cover one of those ideas—which goes by the awesome name of Technicolor—in a later post.)

One thing the Higgs boson is not: it is not the Big Missing Particle that Solves All Problems in physics. It is in no sense a “god particle”. Its presence or absence tells us about the Standard Model, electroweak theory, and something about cosmology—but its potential discovery verifies the predictions of a well-established theory. Even its absence doesn’t damage us too much: we know the SM is not all there is, simply from the existence of dark matter, the fact that the SM doesn’t cover gravity, and so forth.

In the early Universe when things were hot and dense, the electroweak  forces were one force; high-energy particle colliders are capable of accessing aspects of those conditions.

### The Higgs Boson, in Experiment

(For this section, I draw on plenary talks by Mia Tosi, Alex Martyniuk, Wei-Ming Yao, and Dieter Zeppenfeld. Any errors are mine, of course.)

Turning the theory into something that can be tested in particle colliders is a bit challenging. I won’t delve into the whole structure of the detectors in the Large Hadron Collider (LHC), mostly because it’s very involved and I don’t know it very well. However, suffice to say that most particles involved in the experiments are not detected directly, and the Higgs (which is both neutral and short-lived) is no exception. Instead, experimenters track the decay products: photons, stable particles like electrons, and so forth, and a lot of work is required to go from the detection signatures back to the particles that made them. While particle physicists are very good at this process, it’s not simple.

Based on detailed measurements of the top quark and W/Z boson masses at Fermilab, we have an idea of the general mass range in which the Higgs boson should lie (assuming it’s consistent with the SM). The Collider Detector at Fermilab (CDF) along with ATLAS (A Toroidal LHC ApparatuS) and CMS (Compact Muon Solenoid) at the LHC are three independent detectors whose capabilities include Higgs-hunting. Alas, the Tevatron (which contained CDF) shut down in 2011, but as I saw this morning, there’s still some nicely exciting results coming out of its last run.

Based on mass estimates from the SM, Higgs-hunting requires a wide range of energies: 110 to 600 GeV. (1 GeV = 1 billion electron volts, which is a useful unit of energy and for mass in particle physics. For comparison, an electron’s mass is about 500 thousand electron volts, and the proton mass is about 940 million electron volts.) This range involves several possible decay modes for the Higgs boson into other particles. The following is not comprehensive, but rather focuses on the ones we’ll get most excited about:

• Diphoton (γγ channel): the Higgs decays into two gamma-ray photons. This is a relatively small effect, if it occurs, but if it’s seen, it rules out many other particle candidates. For example, no vector particle can decay into two photons.
• Decay into two W bosons (WW channel): this is a nice, sexy option that covers a wide range of energy possibilities.
• Decay into two Z bosons (ZZ top channel): this mostly is important at the higher end of the energy scale.
• Decay into a top quark/antiquark pair (tt channel): significant only at the high end of the scale.

(One thing to remember: the Higgs is neutral, so it must decay into particles with opposite charges or into other neutral particles.)

As it turns out, the diphoton channel has a lot of background noise, but the LHC is good at singling out photons with the energy we care about. Similarly, the WW channel produces a fairly wide signal (meaning: intrinsic error is large, so it’s hard to figure out exactly where the signal is), so we need to know the background properties very well. The ZZ channel is the “gold-plated” mode, according to Zeppenfeld, since it has low noise—and the results rule out any Higgs boson between 320 and 560 GeV. That means the Higgs, if it exists in this range, must lurk toward the low end.

Now anyone who has been paying attention over the last year knows at least part of the story: all three detectors (CDF, ATLAS, and CMS) found small signals above the background at fairly close to the same energy. ATLAS found a bump at 126 GeV, CMS found one at 124 GeV, and CDF discovered a very broad but interesting peak between 115 and 130 GeV. (I apologize that I don’t have all the error sizes, which breaks my rule I expounded at ScienceOnline: without the size of the error, I’m not really reporting all the facts.)

How much can we trust these data? The answer depends on how you look at it. Basically, we want to know what the probability is to find a signal at that particular energy value—as well as what the probability is that we’ll find any energy bump at any energy in the range we’re testing, which is called the “look-elsewhere” probability. The look-elsewhere numbers for the individual detectors aren’t very good: it’s too likely that we’ll find a signal somewhere in the range, but there’s no guarantee it’s real. However, the data look pretty good when you compare all of them together, though how this should be done isn’t clear.

The researchers I talked to were understandably reluctant to say how likely it is for all three experiments to find something at roughly the same energy, but in a sense it doesn’t matter. This year, the LHC will be producing roughly 10 times the data compared to the 2011 results, which I’m writing about here. That extra data will settle one way or the other if the peak around 124-126 GeV is a real signal or not…and whether anything else might be hiding out in the background.

### 14 responses to “The Higgs Boson, in Theory and in Experiment”

1. bryansanctuary

I like two of your comments: first the Higgs boson is not the “god” particle and I think it is too bad that this label has been given. Second if it is found, then it still does not complete our understanding since, as you say, there is still Dark Matter to figure out.

2. […] Merchandise « The Higgs Boson, in Theory and in Experiment […]

3. […] 1 of my dispatches from the Phenomenology 2012 Symposium involved the theory of the Higgs boson, along with a summary of the latest experimental searches for it. Yesterday’s post was less […]

4. […] conference themes will be appearing elsewhere soon, so when it goes live, I’ll link it here. (Part 1 on the Higgs boson and Part 2 on neutrino physics cover two of the major themes of the […]

5. […] is up at Ars Technica. It contains some of the same information as my posts on this site (see Part 1, Part 2, and Part 3), but it also covers the hunt for supersymmetry and attempts to find dark […]

6. […] fill in all the details necessary for a complete understanding. If you want to fully understand the physics of the Higgs boson, you need a lot of physics (including basic quantum mechanics, quantum field theory, and classical […]

7. […] As the rumors hinted all week, this morning (9 AM Central European time, so 3 AM US Eastern time) researchers at CERN announced the discovery of a new particle with a mass of around 125 GeV. (1 GeV = 1 billion electron volts. Particle physicists often use energy units for mass, thanks to Einstein’s famous E = mc2 equation. Electron masses are about 0.5 million eV, and protons are about 940 million eV.) This is consistent with earlier data, but with far more confidence. Results from four different detectors—CDF and DØ at Fermilab, and ATLAS and CMS at CERN—all show the presence of a particle whose mass is about 133 times greater than a proton’s mass. Based on the data, the particle is a scalar particle, electrically neutral, and rapidly decaying, which are all indicative of the Higgs boson. […]

8. […] runs the risk of getting lost. It’s not as triumphant, perhaps—after all, the hunt for the Higgs began decades ago—but it’s still important, especially for cosmologists like […]

9. […] tell how mechanical systems work, but at their most profound, they lead to results such as the Higgs mechanism, by which particles acquire mass. We don’t need to understand particle physics for […]

10. […] option is exotic matter, and we’re not talking about the ordinary exotic matter like the Higgs boson or dark matter, because these are associated with positive energy density. The kind of exotic […]

11. […] Probing matter at its most fundamental requires high energies. We can’t see these particles, even with powerful microscopes: the wavelengths of visible light are much bigger than atoms, so we’ll never see them directly. To get to the constituents of atoms, one of the best ways is to collide particles together and measure what comes out. At sufficiently high energies, if protons collide with each other, they interact on the level of their constituent quarks and gluons. The (unfortunately) now-inoperative Tevatron collider at Fermilab slammed streams of protons and their antiparticle partners, antiprotons, into each other at a high fraction of the speed of light. The huge Collider Detector at Fermilab (CDF) shown above is one of two Tevatron detectors that measured the energy and momentum of particles produced in these high-energy collisions, sifting through the vast number of byproducts to find new particles, new interactions, and ultimately get at the structure of matter at its most basic. CDF and its fellow Tevatron detector DØ (pronounced “D-zero”) found the top quark, the heaviest and most unstable of the quarks; they also contributed to the discovery of the Higgs boson. […]

12. […] known as the Higgs mechanism, and one consequence is the prediction of a new particle, the Higgs boson. The new particle to make CP violation work without breaking QCD is called the […]

13. […] quaternions paved the way to much of the math underlying modern physics, including the theory of the Higgs boson. And though I hardly need to say it, there’s a lot more to Ireland than green clothing (which […]

14. […] The Higgs Boson, in Theory and in Experiment: Some physics background on the Higgs boson, written slightly before the data demonstrated its existence. I wrote this in the midst of a big particle physics conference, in between presentations by and conversations with researchers. […]